Geodesic
A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 637-648 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Given a domain $\Omega $ of class $C^{k,1}$, $k\in \Bbb N $, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega $ in the sense that $(\partial- {\partial x_n})\alpha (x',0)= - N(x')$ and that still is of class $C^{k,1}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class $C^{k,1}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.
Given a domain $\Omega $ of class $C^{k,1}$, $k\in \Bbb N $, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega $ in the sense that $(\partial- {\partial x_n})\alpha (x',0)= - N(x')$ and that still is of class $C^{k,1}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class $C^{k,1}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.
Classification : 35A25, 35A99, 46E35, 46N20, 47A20
Keywords: chart; coordinate transformation; normal vector; normal derivative; extension theorem; Muckenhoupt weight 
@article{CMJ_2009_59_3_a6,
     author = {Schumacher, Katrin},
     title = {A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {637--648},
     year = {2009},
     volume = {59},
     number = {3},
     mrnumber = {2545646},
     zbl = {1218.47019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a6/}
}
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Schumacher, Katrin. A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 637-648. http://geodesic.mathdoc.fr/item/CMJ_2009_59_3_a6/